×
×

# Let X and Y be Bernoulli random variables. Let Z = X+ Y.a. ISBN: 9780073401331 38

## Solution for problem 4E Chapter 4.1

Statistics for Engineers and Scientists | 4th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants Statistics for Engineers and Scientists | 4th Edition

4 5 1 324 Reviews
11
3
Problem 4E

Let X and Y be Bernoulli random variables. Let Z = X+ Y.

a. Show that if X and Y cannot both be equal to 1, then Z is a Bernoulli random variable.

b. Show that if X and Y cannot both be equal to 1, then pz=px+py

c. Show that if X and Y can both be equal to 1, then Z is not a Bernoulli random variable.

Step-by-Step Solution:

Step 1 of 3:

(a)

In this question, we are asked to prove that if and cannot both be equal to 1, then is a Bernoulli random variable.

Let and be Bernoulli random variables. Let = .

Case 1:

If and ,   Case 2:

If and ,   So in both the cases .

The random variable is said to have the Bernoulli distribution when random event results in the success, then . Otherwise .

So from the definition we can say that is also a Bernoulli random variable.

Since value of .

Hence proved.

Step 2 of 3:

(b)

In this question, we are asked to prove that if and cannot both be equal to 1, then From the addition rule of probability, we have =   ……….(1)

Since and cannot both be equal to 1.

Hence ,

we can rewrite equation (1) as, =  , and Substitute above values, we have Hence proved.

Step 3 of 3

##### ISBN: 9780073401331

The full step-by-step solution to problem: 4E from chapter: 4.1 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: Bernoulli, both, show, random, equal. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 4E from 4.1 chapter was answered, more than 1004 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “Let X and Y be Bernoulli random variables. Let Z = X+ Y.a. Show that if X and Y cannot both be equal to 1, then Z is a Bernoulli random variable.________________b. Show that if X and Y cannot both be equal to 1, then pz=px+py________________c. Show that if X and Y can both be equal to 1, then Z is not a Bernoulli random variable.” is broken down into a number of easy to follow steps, and 66 words.

Unlock Textbook Solution